Monday, March 2, 2015

What an awesome idea, the flashblog post. Topic- what is the most off-the-wall lesson you've ever done?

The only thing I can think of is the voicethread I did last year called "What Would the Teacher Say?" in which I showed a step-by-step procedure (mathematical of course) and I asked them to supply the explanatory comments for each step as if they were the teacher. It was a procedure made up of things they already knew about, but applied to a new function. I think I tried to start a new hashtag #wwtts but it didn't take off.

The idea came to me in a flash, I can't even tell you from where. But some kids took me at my word and tried to mimic me, while others went too far into the back ground knowledge and over-explained things. But I'm going to try it again!

Friday, January 30, 2015

Every year, when I start the logarithms unit, I brace myself. I know I'm going to lose a lot of kids. I've tried all kinds of ways to make logs clear. I've written about it here, in fact, and each time I think "This is gonna be great!" but then it's not. But this year, I think I hit on something. I really mean it this time. No really!

And guess why!?!? It's because of the geogebras I've been getting them to create. (If you have no idea what I mean by that, this will give you some idea.) Another unexpected benefit that just kind of fell into my lap. I'm using their exponential geogebras to create suspense about logarithms!

Where we are now

We're currently studying the exponential function, and this time I had them start creating their geogebra explorers very early in the unit, so that they could use them in parallel to the lessons, for pinning things down, validation, exploring, whatever. (Note to self: Do that next year for every function. It's too overwhelming for them to do it all at the end of the unit.)

Anyway, I knew that they'd be able to get their sliders, asymptote, domain etc etc all done, but that when they'd get to the zero, specifically figuring out a formula for it, they'd be at a loss. When I first realized this, I thought, ooh, that might be frustrating or confusing, but then I realized that it would be an opportunity to motivate the need for logs. Just the act of asking me "How do we solve for the x in this?", ie an equation like indicates that they are aware that this is a thing. A new thing. Which let's face it, logs are.

The plot thickens

They haven't done logs, so this kind of makes it suspenseful for them! I'm hoping that in a week or so, when I reveal logs to them for the first time, instead of the usual confusion and horror and OMG THAT'S IT I'M GOING INTO ART, I'll get "Oh! So that's how you solve that equation!" or something like that.

To add to the suspense, I had them spend some time struggling with the question: What can I do to both sides of this equation: , that is the opposite? I wanted to use that kind of language because that's what they are used to - again to motivate that this calls for something totally different. Trying to find that opposite operation, and failing to do so (which they did spectacularly), points them away from that old familiar safe language, which is a good thing. Kids, you're so not in Kansas anymore.

Questionable pedagogy?

It's not completely true that they haven't seen logs, actually, because I have shown them that to solve , they can get the value of x by either trial and error, or by using the log button on their calculator and punching in:

But they have no idea why that works, or what the log button does yet. Normally I don't encourage my students to do something without understanding it, but logs are different. I find the word itself is intimidating and doesn't sound at all like what it is - an exponent. So I get them used to hearing it for a while before actually explaining it. I'm not sure about the pedagogical appropriateness of that....but emotionally I think it helps. And it also lets them know that logs have something to do with solving exponential equations.

My evil plan's results so far

Dr. Eeeevillllll!!!

So far, it has all worked exactly according to plan, at least for a few students. Several students got everything done in their geogebra except for the zero, and asked me to help them figure out the formula for the zero. I of course refused. Nicely though!

Another asked "Are we allowed to use logs to do the zero in our geogebra?" I said sure, in fact, you'll have to, there's no other way! Now I think I should have just batted my eyes, all innocently, and said, "Well, sure, if you think it'll help..."

So the suspense is building, for them and for me! If only one kid figures out how a formula for their zero, all by themselves, I will be thrilled. That'll be better than all preceding years.

Wednesday, October 15, 2014

Last year was the first year I had my students making geogebra applets. Now that I look back, I think I went too fast at first, because their first function assignment was this. I think it was too much too soon. I may have frightened a few of them....so this year,

I'm slowing down now so I can speed up later.

This time around, they did that same linear function geogebra, but in several layers. I devoted a whole week to letting them get to know geogebra, using the linear function, with which they are already familiar from grade 10. I wanted to start with the linear so that this time around, they're learning about geogebra, as opposed to the math. Although frankly, the two never happen in isolation, but I digress. I had them watch my "Learning Geogebra" video, do the practices that went with them, and then create a new geogebra every day of the week, each one a copy of the previous with more information added to it. I gave feedback on every single version, and helped individuals so that everyone was good before going on to next version. Here's what we did:

Day 1: Create a linear function controlled by sliders for slope and initial value & make sure the graph matches with your own knowledge of the linear function (ie increases for a > 0, flat for a = 0, etc)

Day 1: Sliders for a and k, rule y = ax + k

Day 2: Add a t-slider and a point P whose position is controlled by the slider, and which slides along the line, no matter how much a and k are. This was really hard for them, partly because they thought that sliders were only for parameters, which was my fault. Will have to do that better next year.

Day 2: t-slider and point P = (t, at + k)

Day 3: Add the initial value and the zero. Developed formula by: Got them to pick their own a and k, calculate I and Z, then use their own ggb to check. Survey everyone's calculations to get pattern, develop formula for I and Z, type in point to geogebra.

Day 3: I = (0, k) and Z = (-k/a, 0)

Day 4: special stuff, like conditional colours depending on whether the function increases or decreases (or is constant), displaying rule/coordinates using the "show value", or by using text boxes with objects in them.

Day 4: Cool fun pretty stuff

Bonus teachable moment

Some students didn't seem familiar with good computing practices such as saving subsequent versions with a new name, or file naming practices. The version created on day 1 was linear1, day 2 was linear2, etc. I discovered this when one student sighed and said it was tiring having to start all over each time....

And on that note, I made this for them:

And now, for the rest of this year, they're going to make geogebras AND USE THEM!!! To make more!!!!

I want them to do this for EVERY function we're studying. And not only make geogebras, but USE them. And not just because I tell them to, but because they are compelled to, in order to move their own learning forward, in whatever direction they choose. I'm seeing a cyclical formation, in which they use their own paper graphs, their own calculations, and their own instincts to create, use, then improve their geogebras, which then feed the next one...

Tuesday: (Yesterday) Graph, on graph paper, many graphs of absolute value functions, and worked their way up until they could quickly graph and describe y = a |b(x - h)| + k. So now they knew what a graph should look like and why it looks that way.Wednesday: (Today) Create version 1 with sliders for a, b, h, and k, and verify they're doing what they should by comparing to paper graphs. Also put in a vertex with (h, k) and make sure it's where it should be.

Thursday:Math lab! Use version 1 to explore relationships between parameters, to develop point P.Friday: Create version 2 with time slider and point P, verify it using own calculationsNext week: To add initial value, domain, range, interval of increase etc

New Rule: Trust yourself first, geogebra second

What I really, really want to EMPHASIZE is that they verify, as much as possible, their own geogebra, using their own calculations, and not vice versa. Most importantly they verify NOT by showing it to ME and asking ME if it's right.

If this works, by the time they're done this, they will know the absolute value function like a boss!

Sunday, October 5, 2014

I’m an online teacher for LearnQuebec, and I recently became
a student in a classroom again, which hasn't happened in a long time. In my
development as a teacher, I tend to spend a lot of time online, learning new things
independently in a just-in-time fashion, but this post is about an instance in
which that didn't work out, and I needed to be face-to-face with an instructor
and peers. As usual, I learned way more than just what I set out to learn...

Audrey code

Until very recently, the only code I knew was Audrey code.
For example, the first time I asked someone what “html” was, they answered me
by saying “hyper text markup language.” I responded by blinking and saying
thank you, which is Audrey code for “Now I have four more questions in addition
to the one I just asked you.”

*blinks*

Probing further did not help. Every explanation seemed to
make things worse, and intimidate me even more. Brow-furrowing, sighing, and wincing became
part of my code. Nevertheless, I had a vague notion that it had something to do
with the internet.

Coding? What is this coding?

Sometime later, I started seeing hashtags about coding on
twitter, like #kidscancode, #codingforkids, and #coding. There was a lot of
enthusiastic buzz from teachers about the many benefits of coding. Not only is
it fun, addictive, & creative, but it improves understanding in math and languages as well. It was the creative part that interested me
most! I just wasn't sure of what type of
coding everyone was talking about, or what exactly was being created. But I knew that before I tried to get my students to code, I needed to know how to do it myself - teaching usually works out better that way.

I decided to join codeacademy.org and try to learn coding on
my own. I started with JavaScript,
because I had heard it referenced while using my favourite software, geogebra. The
lessons were easy enough to follow, and I made “progress” according to the
site, but I still felt like I was in the dark as far as what I was creating.
Where would I use this JavaScript interactive thingy? I was missing the big
picture, and I just couldn't keep at it without that. I felt constantly distracted, even agitated by that.

Google Apps scripts

Another effort that seemed, at the time, to be unrelated to
html and coding was that I tried to learn how to write google apps script. I
use google forms a lot, and there were specific things I wanted to be able to do
with the data that my students were entering on those google forms. Off I went
to google, and entered their google apps script “tutorials”. The problem here
was that each link lead to so many other links that I lost my way very quickly.
Unlike my codeacademy experience, I was
clear on what I wanted to create, but the tutorials didn't seem organized in a
user-friendly way. In fact, one of the links lead back to codeacademy,
specifically to their JavaScript course, which I’d already tried. What this had
to do with google apps script I didn't know, which added to my confusion.

Convergence at Ladies Learning Code

These mysteries were finally solved for me on Sept 27 at a
workshop in Ottawa called Ladies Learning Code. A friend had happened to
mention to me that Sept 27 was National Ladies Learn to Code Day all across
Canada. LLC (@llcodedotcom) is a not-for-profit Canadian organization devoted
to teaching code to anyone who wants to learn in a comfortable, friendly,
collaborative environment. They were having an introductory one-day workshop in
many cities across Canada on Sept 27, so off I went to register. Unfortunately,
the Montreal one was already full, so I decided to go to the one in Ottawa. I
was persistent, because I was really interested in not only the coding, but the
people who were organizing this amazing event, for free, on their weekend. People are endlessly fascinating to me, especially people who are passionate and creative.

I was not disappointed, in any way! Everyone working at the
LLC session was a volunteer – our instructor, Jessica Eldredge (@jessabean), the mentors (satellite teachers, one for every
4 participants), and the students from U of O. And everyone was friendly. You
could tell right away that they were there to have fun and to help people. My
favourite kind of people! I had a very strong sense that web developers are
highly creative people who love doing what they do. And they love teaching
other people how to do it! As for the participants, most were young, but there
were a few my age, one of which sat at my table – coincidence? Probably not.

I'm sitting just right of centre. Coding!

At last - the Big Picture

Within the first few minutes of the session, a lot of my previous
confusion was cleared up by our instructor, Jessica Eldredge. She said that
html was what created webpages, and that you could think of webpages as being
in three layers, each one in a different type of code:

The first is the content
(text, pictures, links etc) which is created by the html.

The second is the
CSS, which is another language altogether, and which makes the content have a
certain colour or style or placement on the webpage. In other words, it makes
it look pretty.

The third is the interactive elements, such as a gizmo on
explorelearning.com. That’s where code like javascript comes in, and that’s
where I had unwittingly started on my unsuccessful learning-to-code journey
prior to this workshop. No wonder I had been confused – I had started with the
last thing – javascript! Suddenly all the pieces fell into place for me. It
felt like my mind was now truly open.

Workflow:

I
really liked the way that the workshop was organized. It was kind of a mix of
the flipped class and direct instruction. Jessica would spend a few minutes explaining
something, then we would work for a while to complete the accompanying
set of instructions, while getting lots of support from our “mentor.” Each
group of four people had their own mentor. Ours was Gavin (@GavinNL), who was
wonderful. And he happens to be a math and science teacher! He was there in a heartbeat
when we needed him, which was tremendously reassuring, but we also had the
ability to move forward at our own pace as well, because we had already
downloaded, prior to the workshop, all kinds of software and files, including
all of Jessica’s slides and instructions. Hence the flipped element. I feel validated, because I use the flip in my own classes.

Audrey learned to code!

By lunchtime, I had made this:

Incredibly, I had written some html and css, and it had worked! We didn't get to the interactive stuff, but at least now I know what it is, what it's for, and where to go to continue to learn.

What else did I learn?

Learning really is social. It means so much to be able to turn to someone, for a reaction, for help, for reassurance, and to offer it to them. Humans need humans.

I like having the option to move ahead or go back as I wish. And at different times during the day, I did both. Although at around 2:30, my saturated mind ground to a complete halt.

That option to move at one's own pace is only truly available if the material given is well organized, easy to find, and contains good visuals and examples, which Jessica's did.

Hearing someone say something is way more powerful than reading it to yourself.

A webpage is a file! That blew my mind. To see my webpage, I double-clicked on a file with .html at the end. I don't know why that was so eye-opening for me, maybe because it made it all seem a lot less like magic and more like logic.

I need to have the big picture to learn some things. Otherwise, I'm constantly distracted and agitated.

Web developers are highly creative people who are passionate and love to teach other people how to do the same! I'm encouraging my own kids to learn, because they are very creative people too. So far no luck, after all, I'm their mom.

Finally, there are an awful lot of people out there who love to teach, and are really good at it, but very few of them do it for a living like I do. I'm lucky like that.

What's next?

So what am I going to do with this? Not sure yet - I had a vague notion that I would rebuild my own blog from scratch, but that seems like it might be a bit too much to start off with. I remember feeling this way when I started to learn geogebra - I had no idea what to make with it, I just knew that it was really really cool. That's where I am now - any suggestions would be more than welcome! And that's not Audrey code for anything!

Thursday, September 25, 2014

It was one of those classes when I felt like I learned at least as much as they did, and all kinds of unexpected things happened. During class and as I wrote this post.
The idea that I wanted to get across, with as few words as possible: That under certain conditions, for every answer, not only is there is always a question to go with it, but there is only and exactly one question that goes with it.

The exact mathematical version of that, if you're into that: Given a resultant vector, and two other non-collinear vectors, under certain conditions:

1. There is always a way to linearly combine the two to get the resultant.
2. There is only one way to linearly combine the 2 that will work out to that resultant.

This is what we did in class, on the whiteboard, which, remember, is all online, so everybody can write on and see the same board at the same time, and talk to each other while they do.

First I showed them this:

and said: "The red vector is the resultant of some number of blues and some number of greens being added. Since the red vector is the answer, what am I going to ask you to figure out?"

Someone said "The question?" Bingo. In other words, they had to figure out how many blues and greens add up to the red.

I then put them into their breakout rooms (the online equivalent to groups at tables) where they moved the blues and greens around to see how many of each would add up to the red.

Here are a couple of their results:

Everybody got that 6 blues and 4 greens were needed, which was what I expected. I wrote "6 blue + 4 green = red", and talked about how everyone got the same solution...

Audrey's first light bulb moment:

"But," said one student, "we didn't all get the same solution." She explained that really these two solutions weren't equivalent, because the paths from start to finish weren't the same. Light bulb - we're not talking the same language! I'm talking numbers & algebra, and they're talking pictures. It was a great opportunity to clarify exactly what I meant by "solution" right at the start. I meant the total number of blues and the total number of greens, not so much the sequence/path.

So I asked if they thought that there was some other NUMBER of blues and greens that would work, not just a different path but a different numerical combo. I expected and hoped they'd come back with, "Why no Mrs, there isn't any other combo." Back they went. Here was a most interesting result, which lead to

Audrey's second light bulb moment:

...in which there are more than 4 greens and 6 blues, right? TOTALLY awesome. First we traced a path that actually lead to the resultant. Now I got to connect the idea of opposite vectors to subtracting - and establish the convention that if you go one green forward then one back, you've really cancelled out one green with another. Saw a lot of "OOOHHHHH!!!" light bulbs going on everywhere today. We finally agreed that 6 blue and 4 green is the only and simplest numerical solution. Non-verbal idea 2 done!

Now that I'm blogging I can see:

I just loved how all these things came up so naturally and as a result of THEIR manipulations and thoughts - perfectly legitimate and logical thoughts, too. I would never have thought of bringing up any of these issues, which means I would have missed out on making clear the ideas that absolutely needed to be clear before we could move on. Together.

But move on we did. Time for me to mess them up again.

I kept the red, but changed the blues and the greens like so:

Now they're trying to get the exact same answer, but find a different question to go with it - were we only able to get the red the first time using those particular blues and greens that I had lovingly hand picked?

This time, I was not looking for WHAT is the question for this answer so much as IS there a question for it at all. Very quickly I had groups asking if they could change the direction of the blues or greens.

Me: *bats eyes* Well if you insist, I suppose you can make them into their opposites, but that's it.

In fact, it was only possible if the blues got opposite-ed AND you could use part of a blue or green. In fact, the previous discussion on opposites fed into this one very nicely. This lead very naturally into the motivation and meaning for non-whole scalars and negative scalars:

I casually slipped into the notation used for linear combinations, as you can see.

Now that I'm blogging I can see also:

The ease with which they could move the arrows, flip them so they were opposite-ed, and cut them into pieces cranked up the potential a few notches. If I had had them drawing, erasing, etc it would have taken way too long and been way too frustrating, not to mention the colours wouldn't have played a part. It was so much easier to say red, blue, green. Plus it's more fun for them to be manipulating things, and this is as close to observable & active learning as I can get online. Mind you, if I had had any colour-blind students, that would have been a problem.

Back to non-verbal idea 1:

Me: But is it always possible, no matter what blue and green we start with?

Some of them: Yes.

Some of them: No.

I let one group make up their own blues and greens, copy them, and voila, it was still possible. This would be the equivalent of a magician saying pick a card, any card. Now we've established that no matter what the blue and green, we can always get the red using a linear combo of them. Non-verbal idea 1 done.

Under what conditions?

OR CAN WE?!?!? Time to motivate the "under certain conditions" part. For the next part we were all together, no more break out rooms:

I asked how many "a" vectors I would need to make the "c" vector:

Astounding and wonderful to find another hole in their comprehension! Some said 4, or -4, or "You haven't taught us how to multiply and change the direction of the vector." We did some trials together, lining up 4 of them, lining up -4 of them, and eventually agreed that there was no scalar multiple of "a" that would result in "c". Even though they "knew" that collinear vectors are scalar multiples of each other, that's not the same kind of knowing as knowing that non-collinear vectors are NOT scalar multiples of each other, and never will be. I just read that back to myself. Sorry for all the negatives.

Now that I'm blogging...you get the idea:

At this point, I just felt like this lesson/activity/whatever you want to call it, was going really well. So many ideas, so many levels, so much participation, so little time! AND I had at this point stopped using colour-talk, and very sneakily slipped into the proper vocabulary: resultant, collinear, scalar multiple, linear combination. SO I was doing more talking here but I was using official language. This might have been a good time to put in a hinge question, to check that they were all still with me.... next time.

"But," I said, "what if I told you you could use vector a AND some other vector, like this?"

They got this easily, based on the manipulations they'd just done - yes it's possible. But this was another layer of knowing - we'd already established that it's always possible but now they saw that it's actually impossible without the other vector, in order to swing things back to the resultant.

Me: Will it always be possible to get c as the resultant, as long as I have two other vectors to combine linearly?

Them: Yes, Mrs, geez, we get it already.

Me: Really? You sure?

Them: *blink collectively*

Me: *smiles evilly*

Me: What if the other vector was this:

Boom! More OHHHHHH's. Just established what those"certain conditions" are. The two have to be non-collinear, or else you can't swing back toward the resultant.

And the linear combo to go:
If I had had just a little more time in class, I would have moved into this next, but I didn't have time so I assigned a few of this type of question:

What linear combination of <-2, 7> and <1, 4> results in <-1, 26> ?

Next day, the colours paid off:
Many had difficulty, not all, but many. I saw my job as helping them see the question first. Showing how this question was the same as the blue, green, and red arrow questions. In fact, it was really handy to be able to refer to the colours and make this abstract question more concrete that way:n<-2, 7> + m<1, 4> = <-1, 26>

One student said he had tried solving these by trial and error, which at first was easy, but got harder as the examples got harder. He asked if there was a better way. Once he saw that it was a system of linear equations, he and others again went "OOHHHH!" It was an aha moment that algebra really is useful sometimes.

Now to figure out how to do this if I have a colour blind person in my class.

Tuesday, September 16, 2014

Last year I started to wonder what it would be like to teach a new course, because I've taught the same courses for a while now. I guess I made the fates laugh heartily, because guess what happened?!?

This year I'm teaching grade 10 science for the first time. I had taught science and physics in the very distant past, but I am a math teacher by trade and by comfort. New course? Check.

But the science isn't the only new thing. The students in my class happen to be teen moms, who are in a program and a school designed for their particular situation. Which means that they aren't able to do much, if any, homework between classes. So no flipped-class videos either! Whatever happens, has to happen during class. New student situation? Check. New strategy? Check.

AND there is a provincial exam at the end of the year, which they have to pass in order to graduate from high school. Just so long as there isn't too much pressure!

Week one: In which I go to an actual school

Last week was my first week with the girls, and since their school isn't far from here, I drove downtown to meet them face-to-face. (If you're wondering why a teacher would even mention this, just know that I teach online, and don't usually get to meet my students.) We had a friendly chat, and I got to meet their babies, because the nursery is right there in the school. Which one girl said made it hard sometimes, because when you hear your baby cry and you can't go to them, it hurts. I certainly get that.

It was especially important for me to meet these students right away, because if anything is going to get them through this year, it'll be relationships. Sometimes when you're tired and fed up, the only thing that makes you show up is that you like the person or people you're going to see. I hope that's how they'll feel.

Week two: Atoms & baby germs

This week so far has been good in the sense that I've gotten a lot done during class - so far, we've done the different models of the atom, electron configuration, and the periodic table. But there have been a lot of absences already - you know how it is when you're exposed to baby germs, the strongest germs known to man or woman. I really have no idea how to deal with that.

Behold all the science things!

For the last two weeks, it's been Christmas for me. I got to open the Science folder in Smart Notebook's Gallery - woo hoo there's gold in there! And now all those gorgeous geogebras that people made for science? They're mine to covet! That part's been fun - I always felt like science people just had more stuff!

An Act of Love

The greatest impact of all is that I met with the ladies who run this program. They are so passionate, devoted, no-nonsense, and team-oriented that I feel like I've been hit with a lucky stick just to work with them. I've met only a few people in my life that I could honestly say this about, but what these ladies do every day is an act of love. It's hard work, it doesn't pay a lot, it's not glamorous, and sometimes the people you're trying to help only get that long after they've exited the building. But they do it because they love it and they know it's important and they own the job.

This is in response to my answer for Q2, which was about how paperless our classroom is. Now that I am actually thinking about it, I'm not sure mine's as paperless as I thought. Since I teach online, everything that flies between me and my students has to be, at some point, in digital form, but as it turns out, there are wildly varying degrees of paperless-ness during the year. To measure the degree, I'm looking at how much paper is involved in each task at each of these stages:

The actual task

How I deliver that to them

What they do

How they deliver that to me

How I assess

How I deliver that to them

I looked at five different types of tasks, and filled out this table with green = no paper, red = paper. It made it easy for me to see that the most recent things I've been giving them are, or can be at least, 100% paperless.

A little more detail about those tasks:

Tests:

When I give a test, I email it to each of the schools' secretaries, who then prints them up. The students then write on it, and it then gets either scanned or faxed to me. If it's faxed, obviously, there's more paper used. Either way, from then on, it's paperless. I don't put my corrections on any paper. By now their tests are all in digital form, either as an image or a pdf, so I send them to Smart Notebook, where I can mark them up with digital ink, stickers, whatever. Here's how that actually looks in real life:

Assignments:

These might be a worksheet, or a set of problems, or one big multi-step problem (called a situational problem here in Quebec). I deliver it via our CMS (Sakai) but I know most of the students print it up right away. I always give the option to do it on paper, but unlike the tests, they can also do it using some digital tool, such as voicethread, or geogebra, or whatever they choose. I usually offer bonus points for that - questionable I suppose, to motivate using marks, but hey. At any rate, as long as it's presented so that I can follow their reasoning, it's all good. If they go with the paper, then it's exactly the same degree of paperlessness as the test, but if they do it digitally, for example, like this, I create a rubric in Smart Notebook, fill it in with digital ink as I do the tests, export to pdf, then upload that to their dropbox on Sakai. Here's what that looks like to the student:

Blogpost / Geogebra / Portfolio entries:

My students all have their own blogs, as well as digital portfolios. The blogs are of course viewable by anyone, and they are linked from the classblog, but the portfolios are only viewable in our immediate community. Usually the post or the portfolio entry is about an applet they're creating using Geogebra, my favourite dynamic geometry software. Regardless of which of these three they're doing, the degree of paperlessness is the same - 100%!

Toward the end of last year, I gave them a task involving all three of these things. I wanted them to use their portfolios to track their own progress and to get feedback from me, then use geogebra to confirm and organize their learning, and once they were ready to commit, share it with the world on their blogs.

Note that all of these points came directly from the assessment description that I linked above. I didn't want my students to be surprised at how I would be assessing their work! Next year, I plan to get them involved in creating the rubric itself.

I can't show any students' actual portfolios of course, but I did do a post that showed snippets from their reflections for another assignment, this one involving just creating a geogebra. (I got their permission to share, and they're anonymous anyway.) You can read about that here if you're interested to know what I mean by portfolio entries.

Good on paper:

Full disclosure - several times a week, my students write notes, on paper, based on the voicethreads that I create for them to watch. If I put that into the table above, IT WOULD LOOK LIKE THIS. I know it's a lot of paper, but I also find that writing on paper can be a worthwhile thing to do, so I don't know if I'll ever want to change that. I'll reduce, but I don't see myself ever being 100% paper-free. Besides, like my mother, I love books too much!